Demand, Technology, and the Theory of the Firm

Abstract

One of our goals is to understand the forces that influence firm behavior. The principal constraints derive from consumers (demand), nature (technology), and competitors. Demand derives from consumers who strive to maximize their utility or satisfaction within their budget and other constraints. When tastes are under the full control of consumers, firms take market demand as given. That is, demand is exogenously determined. This is the basis of consumer sovereignty—consumer preferences determine what firms produce.

In general, people value assets differently when they are received today versus sometime in the future. When children are given the option of receiving a candy bar now or tomorrow, most want it now. The candy dilemma exhibits a fundamental principle about human behavior—a given asset is generally valued more when received today than in the future. There are many reasons why preferences may exhibit this quality. There is always the risk that we may not be here tomorrow. In addition, most people are impatient. As a person becomes more impatient, he or she will place a higher value on the present.

Given these tendencies, we need to adjust the value of a given asset when received in different periods of time. One way to see how we might account for time differences is to look at how an asset grows in value over time. Given that people place a higher value on current dollars, they must receive some compensation to induce them to loan it to others. Assuming that this rate equals r, the annual rate of return on an investment, then an investment of $x will be worth $y1 in 1 year (or period one) according to the following formula:

Ignoring risk and assuming that all assets earn a rate of r per year, we can work backwards and determine today’s value of any asset worth y1 in 1 year. This is called the present value (PV) of asset y1 that is received 1 year from now. It simply equals x and is calculated as follows:

where D ≡1/(1 + r) is defined as the discount factor, the rate at which a payment next year must be discounted to give us its present value.33 In other words, D represents the present value of $1 received next year.

You can get a better feel for the discount factor by considering extreme values of D. When D = 1, there is no discounting. In this case, $1 received next period is worth $1 today. When D = 0, future dollars are worthless today (i.e., there is no tomorrow). If D = 0.95, then $1 received next period is worth 95¢ today. Thus, D will range from 0 to 1, which can be written as \( D \in \left[ {0,1} \right] \).

To determine the PV of asset y2 when it is received 2 years from now, we must discount it twice. Discounting it one time gives the present value of the asset 1 year from now. Discounting it again gives the present value of the asset today. Thus,

In some problems in finance and economics, it is useful to identify the PV of a stream of payoffs that will be received in every period from today (period 0) to infinity. Assuming the payoff (π) is the same in each period,

Equation (A.10) makes it easy to calculate the present value of a payoff stream that is received each period from today to infinity. For example, if π = $100 and D = 0.9 (i.e., r = 1/9), then PV(π = 100, ∞) = $1,000.